The estate cannot be forced to stop the flights as light aircraft noise is not covered by statutory noise nuisance.
The groups are Friends of the Earth, the Aviation Environment Federation, the National Society for Clean Air, and the Heathrow Association for the Control of Aircraft Noise.
"On one hand, these results are in agreement with our findings from the West London School Study where aircraft noise exposure around Heathrow airport was weakly associated with mental health problems, " she said.
The government currently limits the number of night flights, places restrictions on the noisiest aircraft and sets noise quotas - but these regulations need to be renewed.
Mr Lambourne said the airport's promise of reduced night-time flights and a fining system for aircraft which breached noise limits, offered as a response to the consultation, was "spin".
"The aircraft had to be able to land and take off in 125 meters, it also had to have a very low noise output and the aircraft needed to be able to accelerate rapidly up to 350 mph in order to get point to point at low level very quickly, " said Avcen managing director Mike Dacre.
It said, at the moment, the noisiest aircraft may not be scheduled to land or take off during the "night period" (23:00 to 07:00) and during the "night quota period" (23:30 to 06:00) aircraft movements are limited both by number and by a noise quota.
It also states the applicant did not provide enough evidence to satisfy the council with regards to the scheme's visual impact, construction noise and risk to air traffic control services to aircraft using Robin Hood Airport.
In the early days, airports were not adequately equipped to accommodate these flights, from limited airport staff to a lack of runway lighting to restrictions on noise, but with the increasing need to shuttle aircraft to their next route, seats were made available at deeply discounted rates for passengers willing to make the inconvenient trek.
He singled airplane manufacturer Sukhoi Company, saying Russian made aircraft should be competitive with their foreign rivals in terms of engine noise, fuel economy and flight distance.
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